Uniform Plane Waves Questions and Answers

Answer: C

Correct answer: forty-five degrees

In a good conductor the conduction current overwhelms the displacement current, and the intrinsic impedance becomes \[ \eta = \sqrt{\frac{j\omega\mu}{\sigma}} = \sqrt{\frac{\omega\mu}{\sigma}}\,\angle 45^{\circ}. \] The angle is 45 degrees regardless of frequency - only the magnitude changes with it - and it means the magnetic field lags the electric field by an eighth of a cycle inside the metal.

Answer: D

The dimensionless ratio \( \sigma/(\omega\epsilon) \) decides the classification, and it is frequency dependent: sea water is a conductor at kilohertz and a lossy dielectric at gigahertz. Only the metals remain conductors across the whole radio spectrum.

Answer: A

With no conductivity and no dielectric loss there is nothing to absorb energy, so the amplitude is maintained indefinitely and only the phase advances. Real dielectrics have a small loss tangent and therefore a small but non-zero attenuation.

Answer: B

Writing the permittivity as a complex quantity absorbs both the conduction loss and the dielectric loss into one description, and the tangent of the resulting angle is the loss tangent. Its value decides whether the medium is treated as a dielectric or a conductor.

Answer: C

Correct answer: stays along one fixed direction as the wave advances

Linear polarisation means the electric field oscillates along a single fixed line in the plane transverse to propagation; its magnitude varies sinusoidally and reverses sign, but its direction never rotates. Circular and elliptical polarisation arise when two orthogonal components of unequal phase combine, so that the tip of the vector traces a circle or an ellipse instead.

Answer: D

The resultant vector then has constant magnitude and rotates uniformly, tracing a circle in the wavefront plane. Unequal amplitudes or a phase difference other than ninety degrees give an ellipse, and zero phase difference gives a line.

Answer: A

With the two components in step, or exactly out of step, the resultant stays along a fixed line whose slope is set by the amplitude ratio. Ninety degrees with equal amplitudes gives the circular case, and everything else gives an ellipse.

Answer: B

It is unity for circular polarisation and infinite for linear, so it measures how far a wave departs from the circular case. Antennas intended for satellite links are specified by it, since a mismatch in polarisation costs signal.

Answer: C

The field has no component along the antenna, so no voltage is induced. In practice cross-polar rejection of twenty or thirty decibels is achieved rather than perfect nulling, and that rejection is exploited to reuse a frequency on two polarisations.

Answer: D

Correct answer: \( (\eta_2 - \eta_1)/(\eta_2 + \eta_1) \)

\[ \Gamma = \frac{\eta_2-\eta_1}{\eta_2+\eta_1}. \] The form is the same as the transmission line result with impedances in place of characteristic impedances. Equal impedances give zero, which is the matched case; a perfect conductor has \( \eta_2 = 0 \) and gives \( \Gamma = -1 \), a complete reflection with a phase reversal.